In the case of mega-structures such as tall buildings and long-span bridges, the mitigation of the intensity of the wind excitation through aerodynamic tailoring of the external shape can be fundamental for meeting the performance goals. The search for the best performing shape through an automatic CFD-enabled optimization methodology is potentially less expensive, less time-consuming and more thorough than the common trial-and-error approach based on wind tunnel test results, therefore very attractive. This paper investigates the possibility of carrying out the multi-objective aerodynamic shape optimization of civil structures through an approach in which evolutionary algorithms are used in synergy with ordinary Kriging surrogates. A specifically developed strategy is adopted to update the Kriging models making efficient use of additional CFD runs. Shell scripting, parallelized computations and mesh morphing algorithms are exploited for enhancing the framework's efficiency and consistency. As a case study, the optimization of the shape of a tall building cross-section in terms of both the lift and the drag coefficient is considered.